TABLE OF CONTENTS

FOREWORD

PREFACE

SYMBOLS

Chapter 1 INTRODUCTION

1.1 Plate buckling in steel structures

1.2 Purpose of this book

1.3 Structure of this book

Chapter 2 OVERVIEW OF DESIGN RULES

2.1 Introduction

2.2 Basis of design and modelling

2.3 Shear lag in member design

2.4 Plate buckling effects due to direct stresses (including annexes A and E where applicable)

2.5 Resistance to shear (including annex A where applicable)

2.6 Resistance to transverse loading

2.7 Interaction

2.8 Flange induced buckling

2.9 Stiffeners and detailing

2.10 Reduced stress method (including Annexes A and B where applicable)

2.11 FEM

Chapter 3 CRANE RUNWAY BEAM EXAMPLE

3.1 Description of the crane

3.2 Description of the crane runway beam

3.3 Actions and load partial factors

3.4 Internal forces and stresses

3.5 Verifications in general

3.6 Buckling verifications according to sections 4 to 7, EN 1993-1-5

3.7 Buckling verifications according to section 10, EN 1993-1-5

3.8 Flange induced buckling verification

3.9 Stiffener verifications 3.9.1. Bearing stiffeners

Chapter 4 BOX-GIRDER BRIDGE EXAMPLE

4.1 Description of the bridge

4.2 Internal forces and moments, Stresses

4.3 Web buckling verification for the launching phase

4.4 Effective cross section of the stiffened bottom flange at internal support P1 (uniform compression)

4.5 Effective cross section of the stiffened web at internal support (bending)

4.6 Checking of the box-girder section under bending at support P1

4.7 Shear resistance of the stiffened web panel closest to the internal support P1

4.8 Interaction between bending and shear at support P1

4.9 Intermediate transverse stiffener design

4.10 Buckling verifications at internal support P1 according to section 10, EN 1993-1-5

REFERENCES

Design of Plated Structures

1^st Edition, 2010

Published by:

ECCS – European Convention for Constructional Steelwork

publications@steelconstruct.com

www.steelconstruct.com

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Wilhelm Ernst & Sohn Verlag für Architektur und technische Wissenschaften

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Copyright © 2010 ECCS – European Convention for Constructional Steelwork

ISBN (ECCS): 978-92-9147-100-3

ISBN (Ernst & Sohn): 978-3-433-02980-0

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Foreword

Plated structures are large steel structures commonly made from steel plates welded together. A typical use is for bridge girders and girders for heavy overhead cranes. Compared to steel structures of rolled profiles, plated structures are more prone to local buckling and therefore require design rules to cover such phenomena. In Eurocode 3 such rules are collected in Part 1-5 “Plated structures”, EN 1993-1-5. I was the convener of the project team that wrote the standard, and this team was made up of some very knowledgeable specialists. We spent many years on comparing and finding the best methods of dealing with the most common buckling phenomena. These have attracted a lot of research efforts not only due to some spectacular bridge failures, but also because buckling of plates, and particularly stiffened plates, are scientifically interesting and have attracted the attention of many sharp brains. The result of our efforts was published as a standard in 2006, but the implementation in the different member countries of CEN follows different time tables.

Already before the standard was published we had many requests for background information. The reason was probably that the project team had collected design rules from different sources and chosen the ones that best fitted available information. Some of those were unfamiliar to many engineers and the requests of background information were reasonable. The contract with the EU commission did not include the task of delivering background documents but the academic participants in the project team decided to write one on their own expense. This document can be found on the ECCS web site with the URL http://www.steelconstruct.com/. It is described as a commentary to EN 1993-1-5 and includes background to the design rules and some explanations. There are also some design examples.

As a third step, ECCS has taken on the task of publishing the present manual that you have in your hands. It is intended for engineers who shall apply the rules of EN 1993-1-5 and I have to admit that it is needed. That does not mean that I think we did a bad job with the standard but that the text in the standard is quite brief and in order to interpret it correctly one needs experience and insight in the problems to be dealt with. This manual will be of great importance for engineers to aid them to apply the standard correctly thanks to its explanations and design examples. The authors have done a very good job and after reviewing the text I fully support it as a proper interpretation of the standard.

Bernt Johansson

Professor Emeritus Steel Structures

Preface

Plate buckling related problems in steel structures are inherently linked to complex solution strategies and design procedures. They involve stability analysis in the post-critical state, interaction of different failure modes, imperfection sensitivity, etc.

Eurocode standard EN 1993-1-5 gives a unique opportunity to deal with these problems, at least for typical geometrically more or less regular structural components, by means of fairly simple and consistent set of design procedures, suitable for hand calculations. The main advantage of these design procedures is that generally they were derived from available test results and despite their relative simplicity very often they can be more reliable than advanced numerical simulations. The latter heavily depend on the quality of the applied software tool, the way of modelling, experience of the user, correct interpretation of the results, etc. But even when an experienced design engineer applies advanced numerical simulations for plate buckling problems, a check by means of EN 1993-1-5 design procedures provides comfort and confidence in the results.

The main aim of this Design Manual is to provide practical advice to designers of plated structures for correct and efficient application of EN 1993-1-5 design rules, including several design examples. No deeper theoretical background is given and in this respect the reader is directed to other literature.

The initiative for this Design Manual came from the ECCS that included this Manual into the comprehensive action of preparing the ECCS Eurocode Design Manuals.

The four authors: Darko Beg (University of Ljubljana, Slovenia), Laurence Davaine (SNCF – French National Railway Service), Ulrike Kuhlmann and Benjamin Braun (University of Stuttgart, Germany) worked in close cooperation helping each other and carefully proof-reading parts of the text prepared by other authors. Nonetheless, the leading authors of individual chapters are:

Chapters 2.2, 2.4, 2.9 and all short numerical examples in Chapter 2: Darko Beg

Chapters 1, 2.5, 2.6, 2.10, 3: Ulrike Kuhlmann and Benjamin Braun

Chapters 2.3, 2.7, 2.8, 2.11: Laurence Davaine

Chapter 4: Laurence Davaine and Benjamin Braun

It should be mentioned that Franci Sinur and Blaž ermelj helped in the preparation of the short numerical examples of Chapter 2 and Primož Može and Mojca Jelani helped at the final editing of the text, all four coming from the University of Ljubljana.

At the end of this short Preface it is important to express strong wishes and expectations of the authors that this Manual will find a place on the working desks of design engineers helping them design excellent plated structures. In the authors’ opinion the manual will also be helpful to students of structural engineering on their way of getting familiar with plated structures.

Darko Beg

Ulrike Kuhlmann

Laurence Davaine

Benjamin Braun

Symbols

a	length of a stiffened or unstiffened plate
b	width of a stiffened or unstiffened plate
bf	flange width
bc,loc,i	width of the compressed part of each individual sub-panel i
beff	effective width (for elastic shear lag or local plate buckling)
b1	height of the loaded sub-panel taken as the clear distance between the loaded flange and the longitudinal stiffener
bw	clear width between welds
C	distance between plastic hinges in the flanges
emax	maximum distance from the edge of the stiffener to the centroid of the stiffener
fy	yield strength of steel
fyf	flange yield strength
fyw	web yield strength
hf	distance between mid-planes of flanges
hw	clear web depth between flanges
hwi	clear height of sub-panel i
kF	buckling coefficient for transverse loading
kσ,p	plate buckling coefficient
kτ	shear buckling coefficient of the web between flanges
kτ,i	shear buckling coefficient of sub-panel i
kτsl	shear buckling coefficient of a web stiffened with longitudinal stiffeners
y	effective loaded length
ss	length of stiff bearing
T	thickness of the plate
tf	flange thickness
tw	web thickness
wel	elastic deflection of the stiffener
w0	equivalent geometric imperfection of the stiffener
As	gross cross sectional area of the stiffener
Asl	total area of all the longitudinal stiffeners of a stiffened plate
Ast	gross cross sectional area of one transverse stiffener
Aeff	effective cross sectional area
Ac,eff	effective area of the compression zone of the stiffened or
	unstiffened plate
Ac,eff,loc	effective section areas of all the stiffeners and sub-panels
	that are fully or partially in the compression zone
Asl,eff	sum of the effective sections of all longitudinal stiffeners
	with gross area Asl located in the compression zone
Asl,1	gross cross sectional area of the stiffener and the adjacent
	parts of the plate
Asl,1,eff	effective cross sectional area of the stiffener and adjacent
	parts of the plate with due allowance for plate buckling of
	sub-panels
E	elastic modulus of steel
FEd	design transverse force
FRd	design resistance to transverse loading
Fcr	elastic critical load at transverse loading
Fy	yield load at transverse loading
G	shear elastic modulus
Ip	polar second moment area of the stiffener alone around the edge fixed to the plate
Ist	minimum required second moment of the area of a transverse stiffener to be considered as rigid
It	St. Venant torsional constant of the stiffener alone (without contributing plating)
Iw	warping cross section constant of the stiffener alone around the edge fixed to the plate
Leff	effective length for resistance to transverse forces
Is	sum of the second moment of area of all longitudinal stiffeners
Is,1	second moment of area of the gross cross section of the stiffener and the adjacent parts of the plate, relative to the out-of-plane bending of the plate
Ist	second moment of the area of a stiffener for a cross section for the axis parallel to the web plate
Ist,act	actual second moment of area of the transverse stiffener
MEd	applied design bending moment
Mpl,Rd	design plastic moment resistance of the cross section (irrespective of cross section class)
Mf,Rd	design plastic moment resistance of a cross section consisting of the flanges only
NEd	design axial force
Nst,ten	axial force in the intermediate stiffener imposed by the tension field action
Ncr	Euler elastic critical force
Ncr,st	Euler elastic critical force of the stiffener
VEd	design shear force including shear from torque
Vbw,Rd	contribution from the web to the design shear resistance
Vbf,Rd	contribution from the flanges to the design shear resistance
Vb,Rd	design shear resistance
Weff	effective elastic section modulus
αult,k	minimum load amplifier for the design loads to reach the characteristic value of the resistance
αcr	minimum load amplifier for the design loads to reach the elastic critical value of the plate
β	effective width factor for elastic shear lag
βlt	effective width factor for the effect of shear lag at the ultimate limit state
χc	reduction factor due to column buckling
χF	reduction factor for transverse loading
χw	reduction factor for shear buckling

γM	partial safety factor
η	factor depending on the steel grade
η 1	utilisation level of the design resistance to direct stresses
η 2	utilisation level of the design resistance to transverse loading
η3	utilisation level of the design shear resistance
	slenderness for transverse loading (in EN 1993-1-5 the term “modified slenderness” is used according the Corrigendum (April 2009). In this document a shorter version, i.e. “slenderness”, is systematically used for the sake of simplicity)
	plate slenderness
	reduced plate slenderness
	web slenderness for shear
V	Poisson coefficient of steel
ρ	plate buckling reduction factor
ρx; ρz	reduction factors
ρloc,i	reduction factor for each sub-panel i
σcr,p	elastic critical plate buckling stress
σcr,c	elastic critical column buckling stress
σcr,sl	elastic critical column buckling stress of a single stiffener
σcom,Ed	maximum design compressive stress
σeq,Ed	equivalent design stress
σE	Euler stress
σcr,x; σcr,z; τcr	elastic critical buckling stress
σx,Ed; σz,Ed; τEd	design stresses
τcr	elastic critical shear buckling stress
ψ	stress ratio along edges

Chapter 1

INTRODUCTION

1.1 PLATE BUCKLING IN STEEL STRUCTURES

State-of-the-art steel structures are characterised by a lightweight, slender and fabrication-optimised design. Especially the progress in welding technology since the 1930s has facilitated the increased application of steel plated structures, see Figure 1.1. The significant knowledge gained since then has clearly influenced the design as well as the development of the design standards. With the Eurocodes, harmonised European rules have been established of which standard EN 1993-1-5 “Design of steel structures – Plated structural elements” (CEN, 2006a) deals with the design of plated structural elements in steel structures.

Based on EN 1993-1-5 the designer can choose, considering national allowance, mainly between two different types of design methods according to Fig. 1.2. The effective width method, also comprising resistance models for shear force and transverse force, is very efficient for standard geometries because it accounts not only for the post-critical reserve in a single plate element but also for load shedding between cross sectional elements. The reduced stress method abstains from load shedding between cross sectional elements, but it fully accounts for the post-critical reserve in a single plate element. Beyond that, its general format facilitates its use for serviceability verifications and for the design of non-uniform members such as haunched beams, beam webs with openings and plates with non-orthogonal stiffeners. In addition, a verification methodology based on the finite element method is given in section 2.11. It is the most versatile verification method, however, it requires a lot of experience. It can be used for the determination of the “real” buckling resistance by means of a nonlinear analysis considering imperfections and for the calculation of elastic critical stress values by means of a linear bifurcation analysis.

1.2 PURPOSE OF THIS BOOK

This book intends to provide the designer of steel plated structures with a practically oriented guide to assess EN 1993-1-5 (CEN, 2006a). This design manual is part of a comprehensive series of ECCS publications dealing with accompanying documentation to the Eurocodes. Its aim is to complement the comprehensive theoretical background given in the Commentary to EN 1993-1-5 (Johansson et al, 2007) with practical knowledge for daily usage. Nevertheless, fundamental knowledge of structural mechanics is expected.

This book gives explanations and examples, advice and warnings, all of which intend to give the user considerably more insight and confidence in applying the rules of EN 1993-1-5. In order not to prejudice the use of EN 1993-1-5 where national choices are possible, Eurocode recommendations have been adopted throughout. This has to be kept in mind and, if required, the nationally determined parameters have to be adjusted when applying EN 1993-1-5 in the various member states.

1.3 STRUCTURE OF THIS BOOK

The layout of this book deliberately follows the layout of EN 1993-1-5 in order to allow for easy navigation and reference.

Chapter 2 gives a concise overview of the stability behaviour of plates in steel structures and the corresponding design rules in EN 1993-1-5. Relevant knowledge and terms about load-carrying mechanisms in plates and plated structures under direct stress, shear stress and transverse stress are introduced in order to ease the understanding of the design rules. The main components of Chapter 2 are the explanations of the verification methods which correspond to sections in this book as shown in Figure 1.2. In this book, small design examples in each section address specific issues of these design rules.

In addition, chapters 3 and 4 present two comprehensive design examples of a crane runway beam and a box-girder bridge. In both examples not only the verification methods are illustrated, but also the big picture of the whole design is given. Besides general information on geometry and material properties, firstly loads and governing internal forces are determined. Based on cross section classification, and while adhering to the objective of this book, the examples finally focus on the plate buckling verifications.